The threat of global warming and climate changes is now very real, and greenhouse gas effects have been strongly identified as the major culprit. Such gases emit and absorb infrared (IR) radiation in their molecular spectra, trapping heat in the atmosphere and causing its temperature to rise.

In this talk, the speaker will introduce PDE models for a {m rigorous mathematical} study aiming at problems directly or intimately related to these greenhouse effects. He will first introduce the Schr"odinger equation from laser physics as a basic model. The symmetries of the molecular structures will then be presented. Numerical results (obtained by Dr. Zhigang Zhang of UH) will be illustrated. Finally, relevant issues and interesting problems for research will be discussed.